The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown

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m e paper describes a nonlinear operator, based on Frequency Domain Kurtosis (FDK), that is able to distinguish between transients (impulses and unsteady harmonic components) and stationary sinusoidal signals in background Gaussian noise. For problems involving signal detection in burst noise, filtering by an FDK operator may improve detection results by reducing noise variance and amplifiing narrow-band transient signals.To evaluate the FDK operator's eflciency, direrent processes were considered: impulsive noise and narrowband inteferences in background Gaussian noise and real electromagnetic non-Gaussian noise. The filter robustness is discussed.

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